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A homotopy theory for stacks

Author(s)
Hollander, Sharon Joy, 1975-
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Michael J. Hopkins.
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M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582
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Abstract
We give a homotopy theoretic characterization of stacks on a site C which allows one to think of stacks as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category, that is a formal homotopy theory, in which stacks play the special role of the fibrant objects. This allows us to compare the different definitions of stacks and show that they lead to Quillen equivalent model categories. In addition, these model structures are Quillen equivalent to the S2-nullification of Jardine's model structure on sheaves of simplicial sets on e.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
 
Includes bibliographical references (p. 69-70).
 
Date issued
2001
URI
http://hdl.handle.net/1721.1/8637
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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